Question

What is the common difference for the sequence shown below?

Answer 1

It is B because for every point going down, there is 3 to the left and so it is 1/3 and it has to be negative because its going left

Answer 2

Option 2nd is correct

`-(1)/(3)`

Explanation:

The nth term for the arithmetic sequence is given by:

`a_n = a+(n-1)d`

where,

`a_1` is the first term

d is the common difference

n is the number of terms.

As per the statement:

From the given graph:

At n =1

`a_1 =4`

At n =4

`a_4=3`

Using the nth term formula for the arithmetic sequence:

`a_4 = a_1+3d`

Substitute the given values we have;

`3 = 4+3d`

Subtract 4 from both sides we have;

`-1 = 3d`

Divide both sides by 3 we have;

`-(1)/(3) =d`

or

`d =-(1)/(3)`

Therefore, the common difference for the given sequence as shown is,
`-(1)/(3)`